Models for integrated pest control and their biological implications.

Successful integrated pest management (IPM) control programmes depend on many factors which include host-parasitoid ratios, starting densities, timings of parasitoid releases, dosages and timings of insecticide applications and levels of host-feeding and parasitism. Mathematical models can help us to clarify and predict the effects of such factors on the stability of host-parasitoid systems, which we illustrate here by extending the classical continuous and discrete host-parasitoid models to include an IPM control programme. The results indicate that one of three control methods can maintain the host level below the economic threshold (ET) in relation to different ET levels, initial densities of host and parasitoid populations and host-parasitoid ratios. The effects of host intrinsic growth rate and parasitoid searching efficiency on host mean outbreak period can be calculated numerically from the models presented. The instantaneous pest killing rate of an insecticide application is also estimated from the models. The results imply that the modelling methods described can help in the design of appropriate control strategies and assist management decision-making. The results also indicate that a high initial density of parasitoids (such as in inundative releases) and high parasitoid inter-generational survival rates will lead to more frequent host outbreaks and, therefore, greater economic damage. The biological implications of this counter intuitive result are discussed.